the cost of painting the total surface area of cone at 25 Paisa per centimetre square is rupees 176 find the volume of the cone if its slant height is 25 CM
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Answers
Total cost = Rs. 176
Rate of charge = 25 paise per sq.cm = Rs. 0.25 per sq.cm
Total cost of painting cone = Total surface area of cone * Rate of charge
=> Total surface area of cone = Total cost of painting cone / Rate of charge
= 176/0.25= 704 sq.cm
Let radius of cone be r cm
slant height (l) = 25 cm
Total surface area of cone = πr(r+l)
=> 704 = πr(r+l)
=> 704 = 22r(r+25)/7
=> 704*7/22 = r^2+25r
=> 224 = r^2+25r
=> 0 = r^2+25r-224
=> 0 = r^2+32r-7r-224
=> 0 = r(r+32)-7(r+32)
=> 0 = (r-7)(r+32)
=> 0 = r-7 or 0 = r+32
=> r = 7 or -32
Discarding negative value as radius cannot be negative
Therefore, radius of cone = 7 cm
By Pythagoras Theorem, height of cone = (l^2-r^2)^1/2
= (25^2-7^2)^1/2
= (625-49)^1/2
= (576)^1/2
= 24 cm
Therefore, volume of cone = πr^2h/3
= 22*7*7*24/3*7
= 1232 cu. cm